When Gang of Four guitarist Andy Gill's wife, Time magazine's London Bureau Chief Catherine Mayer, arrives home from work, she gets out a camera to take a picture of myself and her husband together. "I'm fed up having to deny I'm married to you," she explains. I can sympathise, but if she's fed up with the confusion, imagine how Andy and I feel, having now spent three decades denying we're each other.

I probably get the better of the deal: The Other Andy Gill is a damn fine guitarist and producer, a member of an influential band whose style effectively furnished The Red Hot Chilli Peppers with an entire career; so being mistaken for him possibly lends my work a certain unearned cachet. I long since tired of correcting the misapprehension, while for Andy, the final straw came when his own father once complimented him about that fine piece he wrote for The Independent.

It's not hard to see why the confusion arose in the first place. Around the time Gang of Four first attracted attention for the rigorously critical view it applied to music and popular culture, I started writing about music for the NME. "It makes a bit of sense," he concedes, "because some of what you write gels with what I might think on a similar subject." But despite pursuing parallel careers in the same industry, with roughly similar views about the function and value of popular music, we had never once met in over 30 years, until I arrived at his Farringdon apartment this week to interview him and singer Jon King about Gang of Four.

The pair have been friends now for almost four decades, since they were part of a small clique of art students at Sevenoaks School whose number also included the director Paul Greengrass (United 93) and radical docu- mentarist Adam Curtis (The Power of Nightmares). Under visionary art teacher Bob White, this cluster of enquiring minds learned how to interpret the world, their discussions set to a soundtrack of period classics – Dylan, the Velvets, Hendrix – and a few early reggae compilations.

"It was a great refuge, because in my teens I didn't get on well with education," says Gill. "He demanded real commitment from you, and treated you like an adult, which had a massive effect on his pupils."

"He would say, 'What's your idea, pursue your idea, and take it seriously in your own time, don't waste my time'," adds King. "That's when we started thinking seriously about art, and by the time we went up to Leeds University, we had a pretty rigorous approach to art." At Leeds University, their inquisitive attitudes were further fostered by the most radical art department at any British university, a hotbed of Situationism and Structuralism.

In 1976, both friends secured grants for overseas study, but used the money to spend time in New York, where they immersed themselves in the nascent new-wave scene based around CBGBs, becoming friends with members of Television and Patti Smith's group.

"Everybody assumed that we were already in a band, and when we saw Television, we thought, well, if that's a band, then we could certainly be a band," says King. "Then when we came back, British punk had started, which was nothing like the New York art-rock thing, and I think we were more like the New York thing."

Certainly, their musical approach owed little to the speeded-up metal riffs that comprised most punk bands' repertoire. Dr Feelgood were a crucial influence – Gill's guitar style, combining rhythm and lead parts within brusque, slashing riffs, owes a huge debt to the Feelgoods' Wilko Johnson – which they mixed with their love of reggae.

"We liked the earlier ska thing, but dub really blew us away," explains Gill. "We loved its sense of space: compared to pop music, where everything's so densely packed, these huge spaces would emerge – the guitar would drop out, then the bass, leaving the drums, and then this delay would go off, and you knew the bass and guitar would be coming back in but you didn't know when, and when they did it would sound fantastic."

By the time Gill was in his final year at university, the band was signed to EMI and gigging frequently. "We'd be off doing gigs with Siouxsie & the Banshees by night, and by day I'd be writing my dissertation, painting my final show, and in between we'd be writing songs. It was hard work, but stimulating. I'd be writing a song, like "History's Not Made by Great Men", and writing a dissertation on Manet, and the two things would cross-fertilise, ideas from one would end up in the other."

Somehow, they made it all fit together, in a way which possessed the feverish agitation of punk, but also strutted like Memphis funk. Except there was little in Memphis funk – nor, for that matter, in punk – which questioned received attitudes in quite the cerebral rigour of Gang of Four. King, especially, had become fascinated by the deceptions and hidden meanings in the blizzard of messages in magazines, adverts, broadcast media and billboards.

"For example," he explains, "See the girl wearing a bikini/ She's doesn't think so, she's dressed for the H-bomb", lines from a very early song, were based on the two-piece swimsuit deriving its name from the bomb tests at Bikini Atoll. It seemed curious that embedded in our culture was this atrocity, the threat of total annihilation, and this flimsy little thing that girls wear to look fit. It seemed interesting and provocative. The song "Return the Gift" came from another newspaper ad offering a free book, 'yours to keep in any case', if you order a complete set of encyclopaedias – but you're trapped by it, you become a collaborator the moment you agree. That whole idea, of becoming a collaborator, became a kind of mania for us."

It was an issue given substance by a coin which King used to carry around with him, a Vichy franc on which the famous slogan "Liberty, Equality, Fraternity", had been replaced with one which read "Work, Family, Country", a neat summation of the contrast between traditional liberal values and the fascist imperatives imposed by the collaborationist government. "It was all there, embedded on this little coin," he marvels. "Though I remember when I was invited to speak at this Manchester conference on Situationism, I mentioned this coin and got condemned for fetishising the object!"

This sort of leftie Situationist stuff can't have gone down too well in Leeds, which at the time, they acknowledge, was packed full of fascists. "It had always been the heart of English fascism – the biggest Blackshirt demonstration in the 1930s was in Leeds," confirms King. "So whenever we played, there was always a scenario that was likely to happen. It made it quite exciting."

"Being at the heart of the old industrial north in severe decline, it was just ripe for picking by the National Front, and they were there in force," recalls Gill. "It was a grim place, always miserable, always pouring down, and there was a tangible feeling of fear and paranoia on the streets."

"But it was stimulating," maintains King. "You realise where you are and what you're doing, and you want to make your point, in the strongest possible way. You want to say something that's not just confection."

At the time, debates raged on the Left about the correct use of music as a political tool. Roughly speaking, some believed that the simplest slogans – like "We Shall Overcome" and "Give Peace a Chance" – were the most effective, while the more cerebral avant-gardists maintained that this patronised the proletariat, who might be more tellingly emancipated by exposure to more revolutionary musical forms.

"I remember those debates like it was yesterday, and The Gang of Four was in the middle of those two positions," says Gill. "Like when we signed to EMI, it was 'What's that all about?'. People thought we should be on Rough Trade, but we'd gone with the biggest, nastiest, arms-manufacturing company of them all. But to pretend that we didn't want to sell our product would have been dishonest. Anyway, we had already released a record on a small independent label, and never got a penny for it; and though time will tell whether we've been correctly accounted by EMI, they did give us shedloads of dosh in the past."

Quite how much EMI paid them remains to be seen, but along with his subsequent fees as a producer, Gill's earned enough to secure a substantial studio set-up in his Farringdon home. The day I visit, the band have just taken receipt of their first Gold Disc, for 100,000 UK sales of their Entertainment album. It's taken them 30 years, time enough for them to be engaged on their second reunion, this time with a new rhythm section, since original bassist and drummer Dave Allen and Hugo Burnham, who regrouped for their 2005 reunion, now reside permanently in America. This time though, Gill and King are working on material for a new album rather than revisiting old favourites – and not a moment too soon, there being a notable dearth of intelligent, politicised rock around these days.

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